Tiffany is 3 times as old as Emily. Eight years ago, Tiffany was 5 times as old as Emily. How old is Tiffany now?
Explanation: We can use the given information to write down two equations that describe the ages of Tiffany and Emily. Let Tiffany's current age be $t$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $t = 3e$ Eight years ago, Tiffany was $t - 8$ years old, and Emily was $e - 8$ years old. The information in the second sentence can be expressed in the following equation: $t - 8 = 5(e - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = t / 3$ . Substituting this into our second equation, we get: $t - 8 = 5($ $(t / 3)$ $- 8)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 8 = \dfrac{5}{3} t - 40$ Solving for $t$ , we get: $\dfrac{2}{3} t = 32$ $t = \dfrac{3}{2} \cdot 32 = 48$.